Question: Simplify the following expression: $ y = \dfrac{-8}{5} + \dfrac{n - 3}{2n - 2} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2n - 2}{2n - 2}$ $ \dfrac{-8}{5} \times \dfrac{2n - 2}{2n - 2} = \dfrac{-16n + 16}{10n - 10} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{n - 3}{2n - 2} \times \dfrac{5}{5} = \dfrac{5n - 15}{10n - 10} $ Therefore $ y = \dfrac{-16n + 16}{10n - 10} + \dfrac{5n - 15}{10n - 10} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{-16n + 16 + 5n - 15}{10n - 10} $ $y = \dfrac{-11n + 1}{10n - 10}$